Entropy production, fractals, and relaxation to equilibrium

The theory of entropy production in nonequilibrium. Hamiltonian systems, pr eviously described for steady states using partitions of phase space, is he re extended to time dependent systems relaxing to equilibrium. We illustrat e the main ideas by using a simple multibaker model, with some nonequilibri um initial state, and we study its progress toward equilibrium. The central results are (i) the entropy production is governed by an underlying, expon entially decaying fractal structure in phase space, (ii) the rate of entrop y production is largely independent of the scale of resolution used in the partitions, and (iii) the rate of entropy production is in agreement with t he predictions of nonequilibrium thermodynamics.